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<div class="refentry" title="cairo_matrix_t">
<a name="cairo-cairo-matrix-t"></a><div class="titlepage"></div>
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<h2><span class="refentrytitle"><a name="cairo-cairo-matrix-t.top_of_page"></a>cairo_matrix_t</span></h2>
<p>cairo_matrix_t — Generic matrix operations</p>
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<div class="refsynopsisdiv" title="Synopsis">
<a name="cairo-cairo-matrix-t.synopsis"></a><h2>Synopsis</h2>
<pre class="synopsis">                    <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t">cairo_matrix_t</a>;
<span class="returnvalue">void</span>                <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-init" title="cairo_matrix_init ()">cairo_matrix_init</a>                   (<em class="parameter"><code><a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *matrix</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> xx</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> yx</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> xy</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> yy</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> x0</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> y0</code></em>);
<span class="returnvalue">void</span>                <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-init-identity" title="cairo_matrix_init_identity ()">cairo_matrix_init_identity</a>          (<em class="parameter"><code><a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *matrix</code></em>);
<span class="returnvalue">void</span>                <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-init-translate" title="cairo_matrix_init_translate ()">cairo_matrix_init_translate</a>         (<em class="parameter"><code><a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *matrix</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> tx</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> ty</code></em>);
<span class="returnvalue">void</span>                <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-init-scale" title="cairo_matrix_init_scale ()">cairo_matrix_init_scale</a>             (<em class="parameter"><code><a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *matrix</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> sx</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> sy</code></em>);
<span class="returnvalue">void</span>                <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-init-rotate" title="cairo_matrix_init_rotate ()">cairo_matrix_init_rotate</a>            (<em class="parameter"><code><a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *matrix</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> radians</code></em>);
<span class="returnvalue">void</span>                <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-translate" title="cairo_matrix_translate ()">cairo_matrix_translate</a>              (<em class="parameter"><code><a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *matrix</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> tx</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> ty</code></em>);
<span class="returnvalue">void</span>                <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-scale" title="cairo_matrix_scale ()">cairo_matrix_scale</a>                  (<em class="parameter"><code><a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *matrix</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> sx</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> sy</code></em>);
<span class="returnvalue">void</span>                <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-rotate" title="cairo_matrix_rotate ()">cairo_matrix_rotate</a>                 (<em class="parameter"><code><a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *matrix</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> radians</code></em>);
<a class="link" href="cairo-Error-handling.html#cairo-status-t" title="enum cairo_status_t"><span class="returnvalue">cairo_status_t</span></a>      <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-invert" title="cairo_matrix_invert ()">cairo_matrix_invert</a>                 (<em class="parameter"><code><a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *matrix</code></em>);
<span class="returnvalue">void</span>                <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-multiply" title="cairo_matrix_multiply ()">cairo_matrix_multiply</a>               (<em class="parameter"><code><a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *result</code></em>,
                                                         <em class="parameter"><code>const <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *a</code></em>,
                                                         <em class="parameter"><code>const <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *b</code></em>);
<span class="returnvalue">void</span>                <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-transform-distance" title="cairo_matrix_transform_distance ()">cairo_matrix_transform_distance</a>     (<em class="parameter"><code>const <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *matrix</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> *dx</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> *dy</code></em>);
<span class="returnvalue">void</span>                <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-transform-point" title="cairo_matrix_transform_point ()">cairo_matrix_transform_point</a>        (<em class="parameter"><code>const <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *matrix</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> *x</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> *y</code></em>);
</pre>
</div>
<div class="refsect1" title="Description">
<a name="cairo-cairo-matrix-t.description"></a><h2>Description</h2>
<p>
<a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> is used throughout cairo to convert between different
coordinate spaces.  A <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> holds an affine transformation,
such as a scale, rotation, shear, or a combination of these.
The transformation of a point (<code class="literal">x</code>,<code class="literal">y</code>)
is given by:
</p>
<p>
</p>
<pre class="programlisting">
x_new = xx * x + xy * y + x0;
y_new = yx * x + yy * y + y0;
</pre>
<p>
</p>
<p>
The current transformation matrix of a <a class="link" href="cairo-cairo-t.html#cairo-t" title="cairo_t"><span class="type">cairo_t</span></a>, represented as a
<a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a>, defines the transformation from user-space
coordinates to device-space coordinates. See <a class="link" href="cairo-Transformations.html#cairo-get-matrix" title="cairo_get_matrix ()"><code class="function">cairo_get_matrix()</code></a> and
<a class="link" href="cairo-Transformations.html#cairo-set-matrix" title="cairo_set_matrix ()"><code class="function">cairo_set_matrix()</code></a>.
</p>
</div>
<div class="refsect1" title="Details">
<a name="cairo-cairo-matrix-t.details"></a><h2>Details</h2>
<div class="refsect2" title="cairo_matrix_t">
<a name="cairo-matrix-t"></a><h3>cairo_matrix_t</h3>
<pre class="programlisting">typedef struct {
    double xx; double yx;
    double xy; double yy;
    double x0; double y0;
} cairo_matrix_t;
</pre>
<p>
A <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> holds an affine transformation, such as a scale,
rotation, shear, or a combination of those. The transformation of
a point (x, y) is given by:
</p>
<pre class="programlisting">
    x_new = xx * x + xy * y + x0;
    y_new = yx * x + yy * y + y0;
</pre>
<p>
</p>
<div class="variablelist"><table border="0">
<col align="left" valign="top">
<tbody>
<tr>
<td><p><span class="term"><span class="type">double</span> <em class="structfield"><code><a name="cairo-matrix-t.xx"></a>xx</code></em>;</span></p></td>
<td>xx component of the affine transformation
</td>
</tr>
<tr>
<td><p><span class="term"><span class="type">double</span> <em class="structfield"><code><a name="cairo-matrix-t.yx"></a>yx</code></em>;</span></p></td>
<td>yx component of the affine transformation
</td>
</tr>
<tr>
<td><p><span class="term"><span class="type">double</span> <em class="structfield"><code><a name="cairo-matrix-t.xy"></a>xy</code></em>;</span></p></td>
<td>xy component of the affine transformation
</td>
</tr>
<tr>
<td><p><span class="term"><span class="type">double</span> <em class="structfield"><code><a name="cairo-matrix-t.yy"></a>yy</code></em>;</span></p></td>
<td>yy component of the affine transformation
</td>
</tr>
<tr>
<td><p><span class="term"><span class="type">double</span> <em class="structfield"><code><a name="cairo-matrix-t.x0"></a>x0</code></em>;</span></p></td>
<td>X translation component of the affine transformation
</td>
</tr>
<tr>
<td><p><span class="term"><span class="type">double</span> <em class="structfield"><code><a name="cairo-matrix-t.y0"></a>y0</code></em>;</span></p></td>
<td>Y translation component of the affine transformation
</td>
</tr>
</tbody>
</table></div>
</div>
<hr>
<div class="refsect2" title="cairo_matrix_init ()">
<a name="cairo-matrix-init"></a><h3>cairo_matrix_init ()</h3>
<pre class="programlisting"><span class="returnvalue">void</span>                cairo_matrix_init                   (<em class="parameter"><code><a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *matrix</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> xx</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> yx</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> xy</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> yy</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> x0</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> y0</code></em>);</pre>
<p>
Sets <em class="parameter"><code>matrix</code></em> to be the affine transformation given by
<em class="parameter"><code>xx</code></em>, <em class="parameter"><code>yx</code></em>, <em class="parameter"><code>xy</code></em>, <em class="parameter"><code>yy</code></em>, <em class="parameter"><code>x0</code></em>, <em class="parameter"><code>y0</code></em>. The transformation is given
by:
</p>
<pre class="programlisting">
 x_new = xx * x + xy * y + x0;
 y_new = yx * x + yy * y + y0;
</pre>
<p>
</p>
<div class="variablelist"><table border="0">
<col align="left" valign="top">
<tbody>
<tr>
<td><p><span class="term"><em class="parameter"><code>matrix</code></em> :</span></p></td>
<td>a <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a>
</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>xx</code></em> :</span></p></td>
<td>xx component of the affine transformation
</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>yx</code></em> :</span></p></td>
<td>yx component of the affine transformation
</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>xy</code></em> :</span></p></td>
<td>xy component of the affine transformation
</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>yy</code></em> :</span></p></td>
<td>yy component of the affine transformation
</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>x0</code></em> :</span></p></td>
<td>X translation component of the affine transformation
</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>y0</code></em> :</span></p></td>
<td>Y translation component of the affine transformation
</td>
</tr>
</tbody>
</table></div>
</div>
<hr>
<div class="refsect2" title="cairo_matrix_init_identity ()">
<a name="cairo-matrix-init-identity"></a><h3>cairo_matrix_init_identity ()</h3>
<pre class="programlisting"><span class="returnvalue">void</span>                cairo_matrix_init_identity          (<em class="parameter"><code><a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *matrix</code></em>);</pre>
<p>
Modifies <em class="parameter"><code>matrix</code></em> to be an identity transformation.
</p>
<div class="variablelist"><table border="0">
<col align="left" valign="top">
<tbody><tr>
<td><p><span class="term"><em class="parameter"><code>matrix</code></em> :</span></p></td>
<td>a <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a>
</td>
</tr></tbody>
</table></div>
</div>
<hr>
<div class="refsect2" title="cairo_matrix_init_translate ()">
<a name="cairo-matrix-init-translate"></a><h3>cairo_matrix_init_translate ()</h3>
<pre class="programlisting"><span class="returnvalue">void</span>                cairo_matrix_init_translate         (<em class="parameter"><code><a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *matrix</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> tx</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> ty</code></em>);</pre>
<p>
Initializes <em class="parameter"><code>matrix</code></em> to a transformation that translates by <em class="parameter"><code>tx</code></em> and
<em class="parameter"><code>ty</code></em> in the X and Y dimensions, respectively.
</p>
<div class="variablelist"><table border="0">
<col align="left" valign="top">
<tbody>
<tr>
<td><p><span class="term"><em class="parameter"><code>matrix</code></em> :</span></p></td>
<td>a <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a>
</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>tx</code></em> :</span></p></td>
<td>amount to translate in the X direction
</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>ty</code></em> :</span></p></td>
<td>amount to translate in the Y direction
</td>
</tr>
</tbody>
</table></div>
</div>
<hr>
<div class="refsect2" title="cairo_matrix_init_scale ()">
<a name="cairo-matrix-init-scale"></a><h3>cairo_matrix_init_scale ()</h3>
<pre class="programlisting"><span class="returnvalue">void</span>                cairo_matrix_init_scale             (<em class="parameter"><code><a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *matrix</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> sx</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> sy</code></em>);</pre>
<p>
Initializes <em class="parameter"><code>matrix</code></em> to a transformation that scales by <em class="parameter"><code>sx</code></em> and <em class="parameter"><code>sy</code></em>
in the X and Y dimensions, respectively.
</p>
<div class="variablelist"><table border="0">
<col align="left" valign="top">
<tbody>
<tr>
<td><p><span class="term"><em class="parameter"><code>matrix</code></em> :</span></p></td>
<td>a <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a>
</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>sx</code></em> :</span></p></td>
<td>scale factor in the X direction
</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>sy</code></em> :</span></p></td>
<td>scale factor in the Y direction
</td>
</tr>
</tbody>
</table></div>
</div>
<hr>
<div class="refsect2" title="cairo_matrix_init_rotate ()">
<a name="cairo-matrix-init-rotate"></a><h3>cairo_matrix_init_rotate ()</h3>
<pre class="programlisting"><span class="returnvalue">void</span>                cairo_matrix_init_rotate            (<em class="parameter"><code><a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *matrix</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> radians</code></em>);</pre>
<p>
Initialized <em class="parameter"><code>matrix</code></em> to a transformation that rotates by <em class="parameter"><code>radians</code></em>.
</p>
<div class="variablelist"><table border="0">
<col align="left" valign="top">
<tbody>
<tr>
<td><p><span class="term"><em class="parameter"><code>matrix</code></em> :</span></p></td>
<td>a <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a>
</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>radians</code></em> :</span></p></td>
<td>angle of rotation, in radians. The direction of rotation
is defined such that positive angles rotate in the direction from
the positive X axis toward the positive Y axis. With the default
axis orientation of cairo, positive angles rotate in a clockwise
direction.
</td>
</tr>
</tbody>
</table></div>
</div>
<hr>
<div class="refsect2" title="cairo_matrix_translate ()">
<a name="cairo-matrix-translate"></a><h3>cairo_matrix_translate ()</h3>
<pre class="programlisting"><span class="returnvalue">void</span>                cairo_matrix_translate              (<em class="parameter"><code><a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *matrix</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> tx</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> ty</code></em>);</pre>
<p>
Applies a translation by <em class="parameter"><code>tx</code></em>, <em class="parameter"><code>ty</code></em> to the transformation in
<em class="parameter"><code>matrix</code></em>. The effect of the new transformation is to first translate
the coordinates by <em class="parameter"><code>tx</code></em> and <em class="parameter"><code>ty</code></em>, then apply the original transformation
to the coordinates.
</p>
<div class="variablelist"><table border="0">
<col align="left" valign="top">
<tbody>
<tr>
<td><p><span class="term"><em class="parameter"><code>matrix</code></em> :</span></p></td>
<td>a <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a>
</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>tx</code></em> :</span></p></td>
<td>amount to translate in the X direction
</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>ty</code></em> :</span></p></td>
<td>amount to translate in the Y direction
</td>
</tr>
</tbody>
</table></div>
</div>
<hr>
<div class="refsect2" title="cairo_matrix_scale ()">
<a name="cairo-matrix-scale"></a><h3>cairo_matrix_scale ()</h3>
<pre class="programlisting"><span class="returnvalue">void</span>                cairo_matrix_scale                  (<em class="parameter"><code><a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *matrix</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> sx</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> sy</code></em>);</pre>
<p>
Applies scaling by <em class="parameter"><code>sx</code></em>, <em class="parameter"><code>sy</code></em> to the transformation in <em class="parameter"><code>matrix</code></em>. The
effect of the new transformation is to first scale the coordinates
by <em class="parameter"><code>sx</code></em> and <em class="parameter"><code>sy</code></em>, then apply the original transformation to the coordinates.
</p>
<div class="variablelist"><table border="0">
<col align="left" valign="top">
<tbody>
<tr>
<td><p><span class="term"><em class="parameter"><code>matrix</code></em> :</span></p></td>
<td>a <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a>
</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>sx</code></em> :</span></p></td>
<td>scale factor in the X direction
</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>sy</code></em> :</span></p></td>
<td>scale factor in the Y direction
</td>
</tr>
</tbody>
</table></div>
</div>
<hr>
<div class="refsect2" title="cairo_matrix_rotate ()">
<a name="cairo-matrix-rotate"></a><h3>cairo_matrix_rotate ()</h3>
<pre class="programlisting"><span class="returnvalue">void</span>                cairo_matrix_rotate                 (<em class="parameter"><code><a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *matrix</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> radians</code></em>);</pre>
<p>
Applies rotation by <em class="parameter"><code>radians</code></em> to the transformation in
<em class="parameter"><code>matrix</code></em>. The effect of the new transformation is to first rotate the
coordinates by <em class="parameter"><code>radians</code></em>, then apply the original transformation
to the coordinates.
</p>
<div class="variablelist"><table border="0">
<col align="left" valign="top">
<tbody>
<tr>
<td><p><span class="term"><em class="parameter"><code>matrix</code></em> :</span></p></td>
<td>a <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a>
</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>radians</code></em> :</span></p></td>
<td>angle of rotation, in radians. The direction of rotation
is defined such that positive angles rotate in the direction from
the positive X axis toward the positive Y axis. With the default
axis orientation of cairo, positive angles rotate in a clockwise
direction.
</td>
</tr>
</tbody>
</table></div>
</div>
<hr>
<div class="refsect2" title="cairo_matrix_invert ()">
<a name="cairo-matrix-invert"></a><h3>cairo_matrix_invert ()</h3>
<pre class="programlisting"><a class="link" href="cairo-Error-handling.html#cairo-status-t" title="enum cairo_status_t"><span class="returnvalue">cairo_status_t</span></a>      cairo_matrix_invert                 (<em class="parameter"><code><a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *matrix</code></em>);</pre>
<p>
Changes <em class="parameter"><code>matrix</code></em> to be the inverse of its original value. Not
all transformation matrices have inverses; if the matrix
collapses points together (it is <em class="firstterm">degenerate</em>),
then it has no inverse and this function will fail.
</p>
<div class="variablelist"><table border="0">
<col align="left" valign="top">
<tbody>
<tr>
<td><p><span class="term"><em class="parameter"><code>matrix</code></em> :</span></p></td>
<td>a <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a>
</td>
</tr>
<tr>
<td><p><span class="term"><span class="emphasis"><em>Returns</em></span> :</span></p></td>
<td> If <em class="parameter"><code>matrix</code></em> has an inverse, modifies <em class="parameter"><code>matrix</code></em> to
 be the inverse matrix and returns <a class="link" href="cairo-Error-handling.html#CAIRO-STATUS-SUCCESS:CAPS"><code class="literal">CAIRO_STATUS_SUCCESS</code></a>. Otherwise,
 returns <a class="link" href="cairo-Error-handling.html#CAIRO-STATUS-INVALID-MATRIX:CAPS"><code class="literal">CAIRO_STATUS_INVALID_MATRIX</code></a>.
</td>
</tr>
</tbody>
</table></div>
</div>
<hr>
<div class="refsect2" title="cairo_matrix_multiply ()">
<a name="cairo-matrix-multiply"></a><h3>cairo_matrix_multiply ()</h3>
<pre class="programlisting"><span class="returnvalue">void</span>                cairo_matrix_multiply               (<em class="parameter"><code><a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *result</code></em>,
                                                         <em class="parameter"><code>const <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *a</code></em>,
                                                         <em class="parameter"><code>const <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *b</code></em>);</pre>
<p>
Multiplies the affine transformations in <em class="parameter"><code>a</code></em> and <em class="parameter"><code>b</code></em> together
and stores the result in <em class="parameter"><code>result</code></em>. The effect of the resulting
transformation is to first apply the transformation in <em class="parameter"><code>a</code></em> to the
coordinates and then apply the transformation in <em class="parameter"><code>b</code></em> to the
coordinates.
</p>
<p>
It is allowable for <em class="parameter"><code>result</code></em> to be identical to either <em class="parameter"><code>a</code></em> or <em class="parameter"><code>b</code></em>.
</p>
<div class="variablelist"><table border="0">
<col align="left" valign="top">
<tbody>
<tr>
<td><p><span class="term"><em class="parameter"><code>result</code></em> :</span></p></td>
<td>a <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> in which to store the result
</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>a</code></em> :</span></p></td>
<td>a <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a>
</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>b</code></em> :</span></p></td>
<td>a <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a>
</td>
</tr>
</tbody>
</table></div>
</div>
<hr>
<div class="refsect2" title="cairo_matrix_transform_distance ()">
<a name="cairo-matrix-transform-distance"></a><h3>cairo_matrix_transform_distance ()</h3>
<pre class="programlisting"><span class="returnvalue">void</span>                cairo_matrix_transform_distance     (<em class="parameter"><code>const <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *matrix</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> *dx</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> *dy</code></em>);</pre>
<p>
Transforms the distance vector (<em class="parameter"><code>dx</code></em>,<em class="parameter"><code>dy</code></em>) by <em class="parameter"><code>matrix</code></em>. This is
similar to <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-transform-point" title="cairo_matrix_transform_point ()"><code class="function">cairo_matrix_transform_point()</code></a> except that the translation
components of the transformation are ignored. The calculation of
the returned vector is as follows:
</p>
<p>
</p>
<pre class="programlisting">
dx2 = dx1 * a + dy1 * c;
dy2 = dx1 * b + dy1 * d;
</pre>
<p>
</p>
<p>
Affine transformations are position invariant, so the same vector
always transforms to the same vector. If (<em class="parameter"><code>x1</code></em>,<em class="parameter"><code>y1</code></em>) transforms
to (<em class="parameter"><code>x2</code></em>,<em class="parameter"><code>y2</code></em>) then (<em class="parameter"><code>x1</code></em>+<em class="parameter"><code>dx1</code></em>,<em class="parameter"><code>y1</code></em>+<em class="parameter"><code>dy1</code></em>) will transform to
(<em class="parameter"><code>x1</code></em>+<em class="parameter"><code>dx2</code></em>,<em class="parameter"><code>y1</code></em>+<em class="parameter"><code>dy2</code></em>) for all values of <em class="parameter"><code>x1</code></em> and <em class="parameter"><code>x2</code></em>.
</p>
<div class="variablelist"><table border="0">
<col align="left" valign="top">
<tbody>
<tr>
<td><p><span class="term"><em class="parameter"><code>matrix</code></em> :</span></p></td>
<td>a <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a>
</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>dx</code></em> :</span></p></td>
<td>X component of a distance vector. An in/out parameter
</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>dy</code></em> :</span></p></td>
<td>Y component of a distance vector. An in/out parameter
</td>
</tr>
</tbody>
</table></div>
</div>
<hr>
<div class="refsect2" title="cairo_matrix_transform_point ()">
<a name="cairo-matrix-transform-point"></a><h3>cairo_matrix_transform_point ()</h3>
<pre class="programlisting"><span class="returnvalue">void</span>                cairo_matrix_transform_point        (<em class="parameter"><code>const <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a> *matrix</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> *x</code></em>,
                                                         <em class="parameter"><code><span class="type">double</span> *y</code></em>);</pre>
<p>
Transforms the point (<em class="parameter"><code>x</code></em>, <em class="parameter"><code>y</code></em>) by <em class="parameter"><code>matrix</code></em>.
</p>
<div class="variablelist"><table border="0">
<col align="left" valign="top">
<tbody>
<tr>
<td><p><span class="term"><em class="parameter"><code>matrix</code></em> :</span></p></td>
<td>a <a class="link" href="cairo-cairo-matrix-t.html#cairo-matrix-t" title="cairo_matrix_t"><span class="type">cairo_matrix_t</span></a>
</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>x</code></em> :</span></p></td>
<td>X position. An in/out parameter
</td>
</tr>
<tr>
<td><p><span class="term"><em class="parameter"><code>y</code></em> :</span></p></td>
<td>Y position. An in/out parameter
</td>
</tr>
</tbody>
</table></div>
</div>
</div>
<div class="refsect1" title="See Also">
<a name="cairo-cairo-matrix-t.see-also"></a><h2>See Also</h2>
<a class="link" href="cairo-cairo-t.html#cairo-t" title="cairo_t"><span class="type">cairo_t</span></a>
</div>
</div>
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